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EL THE OFFICIAL JOURNAL OF THE FIBONACCI ASSOCIATION

TABLE OF CONTENTS On the Number of Independent Sets of Nodes

in a Tree R. Button, N. Chandrasekharan, andR. Brigham 98

105

112 121

Carlitz Generalizations of Lucas and Lehmer Sequences A.G. Shannon andR.S. Melham

Determining the Dimension of Fractals Generated by Pascal's Triangle Ashley Melia Reiter

Triple Factorization of Some Riordan Matrices Paul Peart and Leon Woodson Three-Square Theorem as an Application of Andrews'

Identity S. Bhargava, Chandrashekar Adiga, andD.D. Somashekara 129 Fourth International Conference Proceedings 133 Some Polynomial Identities for the Fibonacci and

Lucas Numbers Derek Jennings 134 A Variation on the Two-Digit Kaprekar Routine Anne Ludington Young 138 Announcement on Sixth International Conference 145 On Consecutive Niven Numbers Curtis Cooper and Robert E. Kennedy 146 Author and Title Index for Sale 151 Mixed Fermat Convolutions Gospava B. Dordevic 152 Hyperspaces and Fibonacci Numbers Herman Haase 158 Editor's Leave of Absence 161 A Disjoint System of Linear Recurring Sequences Generated by un+2 = un+i + un

which Contains Every Natural Number Joachim Zdllner 162 Generalized Pascal Triangles and Pyramids Their Fractals

Graphs and Applications .Boris A. Bondarenko 165 Associated Sequences of General Order A.F. Horadam 166 Nonexistence of Even Fibonacci Pseudoprimes of the 1st Kind Adina Di Porto 173 The Moment Generating Function of the Geometric Distribution

of Order k .Michael J. J. Barry andAnthonly J. Lo Bello 178

Elementary Problems and Solutions .Edited by Stanley Rabinowitz 181 Advanced Problems and Solutions Edited by Raymond E. Whitney 187

l_ I voi VOLUME 31 MAY 1993 NUMBER 2

PURPOSE The primary function of THE FIBONACCI QUARTERLY is to serve as a focal point for

widespread interest in the Fibonacci and related numbers, especially with respect to new results, research proposals, challenging problems, and innovative proofs of old ideas.

EDITORIAL POLICY THE FIBONACCI QUARTERLY seeks articles that are intelligible yet stimulating to its

readers, most of whom are university teachers and students. These articles should be lively and well motivated, with new ideas that develop enthusiasm for number sequences or the explora-tion of number facts. Illustrations and tables should be wisely used to clarify the ideas of the manuscript. Unanswered questions are encouraged, and a complete list of references is ab-solutely necessary.

SUBMITTING AN ARTICLE Articles should be submitted in the format of the current issues of THE FIBONACCI

QUARTERLY. They should be typewritten or reproduced typewritten copies, that are clearly readable, double spaced with wide margins and on only one side of the paper. The full name and address of the author must appear at the beginning of the paper directly under the title. Il-lustrations should be carefully drawn in India ink on separate sheets of bond paper or vellum, approximately twice the size they are to appear in print. Since the Fibonacci Association has adopted Fi = F2 = 1, Fn+i = Fn + Fn~i, n> 2 and Li = l, L2 = 3, Ln+i = Ln + Ln-i, n > 2 as the stan-dard definitions for The Fibonacci and Lucas sequences, these definitions should not be a paiit of future papers. However, the notations must be used. One to three complete A.M.S. classification numbers must be given directly after references or on the bottom of the last page. Papers without classification numbers will be returned.

Two copies of the manuscript should be submitted to: GERALD E. BERGUM, EDITOR, THE FIBONACCI QUARTERLY, DEPARTMENT OF COMPUTER SCIENCE, SOUTH DAKOTA STATE UNIVERSITY, BOX 2201, BROOKINGS, SD 57007-1596.

Authors are encouraged to keep a copy of their manuscripts for their own files as protection against loss. The editor will give immediate acknowledgment of all manuscripts received.

SUBSCRIPTIONS, ADDRESS CHANGE, AND REPRINT INFORMATION Address all subscription correspondence, including notification of address change, to:

RICHARD VINE, SUBSCRIPTION MANAGER, THE FIBONACCI ASSOCIATION, SAN-TA CLARA UNIVERSITY, SANTA CLARA, CA 95053.

Requests for reprint permission should be directed to the editor. However, general permission is granted to members of The Fibonacci Association for noncommercial reproduction of a limited quantity of individual articles (in whole or in part) provided complete reference is made to the source.

Annual domestic Fibonacci Association membership dues, which include a subscription to THE FIBONACCI QUARTERLY, are $35 for Regular Membership, $40 for Library, $45 for Sustaining Membership, and $70 for Institutional Membership; foreign rates, which are based on international mailing rates, are somewhat higher than domestic rates; please write for details. THE FIBONACCI QUARTERLY is published each February, May, August and November.

All back issues of THE FIBONACCI QUARTERLY are available in microfilm or hard copy format from UNIVERSITY MICROFILMS INTERNATIONAL, 300 NORTH ZEEB ROAD, DEPT. P.R., ANN ARBOR, MI 48106. Reprints can also be purchased from UMI CLEARING HOUSE at the same address.

©1993 by The Fibonacci Association

All rights reserved, including rights to this journal issue as a whole and, except where otherwise noted,

rights to each individual contribution.

l$jie Fibonacci Quarterly Founded in 1963 by Verner E. Hoggatt, Jr. (1921-1980)

and Br. Alfred Brousseau (1907-1988)

THE OFFICIAL JOURNAL OF THE FIBONACCI ASSOCIATION DEVOTED TO THE STUDY

OF INTEGERS WITH SPECIAL PROPERTIES

EDITOR GERALD E. BERGUM, South Dakota State University, Brookings, SD 57007-1596

ASSISTANT EDITORS MAXEY BROOKE, Sweeny, TX 77480 JOHN BURKE, Gonzaga University, Spokane, WA 99258 LEONARD CARLITZ, Duke University, Durham, NC 27706 HENRY W. GOULD, West Virginia University, Morgantown, WV 26506 A.P. HILLMAN, University of New Mexico, Albuquerque, NM 87131 A.F. HORADAM, University of New England, Armidale, N.S.W. 2351, Australia CLARK KIMBERLING, University of Evansville, Evansville, IN 47722 DAVID A. KLARNER, University of Nebraska, Lincoln, NE 68588 RICHARD MOLLIN, University of Calgary, Calgary T2N 1N4, Alberta, Canada GARY L. MULLEN, The Pennsylvania State University, University Park, PA 16802 SAMIH OBAID, San Jose State University, San Jose, CA 95192 NEVILLE ROBBINS, San Francisco State University, San Francisco, CA 94132 DONALD W. ROBINSON, Brigham Young University, Provo, UT 84602. LAWRENCE SOMER, Catholic University of America, Washington, D.C. 20064 M.N.S. SWAMY, Concordia University, Montreal H3C1M8, Quebec, Canada D.E. THORO, San Jose State University, San Jose, CA 95192 ROBERT F. TICHY, Technical University, Graz, Austria WILLIAM WEBB, Washington State University, Pullman, WA 99164-2930

BOARD OF DIRECTORS THE FIBONACCI ASSOCIATION

CALVIN LONG (President) Washington State University, Pullman, WA 99164-2930 G.L. ALEXANDERSON Santa Clara University, Santa Clara, CA 95053 ANDREW GRANVILLE University of Georgia, Athens, GA 30601-3024 PETER HAGIS, JR. Temple University, Philadelphia, PA 19122 FRED T. HOWARD Wake Forest University, Winston-Salem, NC 27109 MARJORIE JOHNSON (Secretary-Treasurer) 665 Fairlane Avenue, Santa Clara, CA 95051 LESTER LANGE San Jose State University, San Jose, CA 95192 THERESA VAUGHAN University of North Carolina, Greensboro, NC 27412